Poincare and logarithmic Sobolev inequality for Ginzburg-landau processes in random environment

• 成果类型: Article
• 署名作者: Landim, C; Neto, JN
• 署名单位: Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0370-y
• 发表日期: 2005
• 页码: 229-260
• 关键词: lattice-gas dynamics; spectral gap; kawasaki dynamics; equilibrium; constant

摘要

We consider reversible, conservative Ginzburg-Landau processes in a random environment, whose potential are bounded perturbations of the Gaussian potential, evolving on a d-dimensional cube of length L. We prove in all dimensions that the spectral gap of the generator and the logarithmic Sobolev constant are of order L-2 almost surely with respect to the environment.